Place berries in a food processor and process until smooth, scraping down the sides as necessary. Add sugar and orange juice; process for a few seconds. Add yogurt and pulse several times until blended. Transfer to a bowl. Cover and refrigerate until chilled, about 1 hour or overnight.

Pour the strawberry mixture into an ice cream maker and freeze according to manufacturer's directions. Serve immediately or transfer to a storage container and let harden in the freezer for 1 to 1 1/2 hours. Serve in chilled dishes.